154/BBDF. problem / Math - Solved Math Problems

MR-154 / 23. problem

Determine the first derivative of the function below:

$y = \frac{2 x}{x^{2} - 1}$

$y = \frac{2 x}{x^{2} - 1}$

$y = \frac{2 x}{x^{2} - 1} = \frac{u}{v}$

$u = 2 x; u^{'} = 2$

$v = x^{2} - 1; v^{'} = 2 x$

$y^{'} = \frac{u^{'} v - u v^{'}}{v^{2}}$

$y^{'} = \frac{2 \cdot (x^{2} - 1) - 2 x \cdot 2 x}{{(x^{2} - 1)}^{2}}$

$y^{'} = \frac{2 x^{2} - 2 - 4 x^{2}}{{(x^{2} - 1)}^{2}}$

$y^{'} = \frac{- 2 x^{2} - 2}{{(x^{2} - 1)}^{2}}$

MathReference - Problems